How to play Kakuro

Crossing sums, not Sudoku lines. Follow the diagonal clues and let two runs narrow each white cell.

This original lesson is separate from saved play. Return to your board’s tab to keep its Undo history.

White cells, blocks and diagonal clues

Use digits 1–9 on every size. Total size includes blocks and clue cells. Only white cells take entries or notes; there are no fixed given digits. Every white belongs to one contiguous Across run and one contiguous Down run, each 2–9 cells long.

TOP-RIGHT = Across, for the run to the RIGHT. LOWER-LEFT = Down, for the run BELOW. Both numbers may appear in one clue cell; absent clues are not shown as zero. The run stops at the next block or board edge. Add its digits to meet its clue, without repeating a digit within that run.

For example a two-cell sum of 4 can only use 1 and 3, in either order; 2 + 2 is forbidden. Matching digits in separate runs across blocks are legal, even on the same visual row or column. There are no Sudoku boxes or whole-row 1–9 requirements.

An original three-by-three teaching board

This total 3 × 3 diagram is an unsupported teaching size, not a playable identity or production-generation fixture. There are four white cells and no givens. Letters A–D mark their locations, not digits. This small lesson has one solution.


	A	B
	C	D

A + B = 4 with distinct positive digits, so A and B are 1 and 3 in some order.
A + C = 3, so A and C are 1 and 2. At the crossing A is in both {1,3} and {1,2}: only 1 remains. Enter A = 1.
The Across 4 now needs B = 3. The Down 3 needs C = 2.
The Across 6 now needs D = 4. Independently check the Down 7: B + D = 3 + 4 = 7. Every run has different digits.

1	3
2	4

These are logical consequences of the clues, not a selected answer reveal. On larger boards you may need more combination reductions before a crossing becomes forced.

Four checked rules

Run combinations

List distinct-digit subsets of this run’s length and printed sum, containing its placed digits. An unfilled cell cannot use placed or unsupported digits. Use 1–9 on every board size.

Crossing run intersection

Intersect the Across and Down combination supports. If both have several digits but share just one, that crossing has one candidate. The preceding checked chain supplies any earlier reductions.

One remaining candidate

Place a digit only when the checked candidate mask for this white cell has exactly one bit left. This is a logical consequence, not a digit selected from the admitted answer.

Supported run assignments

Consider all distinct-digit positional assignments that sum to the clue and respect every current checked candidate mask. Remove a candidate with no supporting assignment. Player notes never restrict these assignments.

Hints show an ordered checked chain beginning at your current entries. Later steps may depend on earlier reductions. Candidate masks use bits 1–9; notes never restrict the engine’s candidates. Easy uses combinations, intersections and forced cells; Medium can require run-assignment support after Easy stalls. No Hard rule is claimed. New offers only total 5 / Easy; the other eight choices are not qualified. These are technical repertoires, not human-difficulty promises.

Keyboard, touch, notes and recovery

Select a white cell, then use the pad or type 1–9. Arrows skip blocks; N toggles notes; Delete, Backspace or 0 erases. Hold a pad digit to inspect it; Shift plus a digit locks its highlight, and Space enters that digit or toggles its note. Undo/Redo restore one recorded move. Blocks and clues never take focus as entry cells.

Automatic note cleanup removes a placed digit only from its two actual contiguous runs, never the whole visual row or column across a block. Notes are sorted possibilities on blank white cells. Check marks wrong entries without erasing them. Wrong but shaped saves remain recoverable.

A forced hint permits one undoable placement. A candidate-only hint explains reductions; Apply removes matching existing notes together as one Undo record. With no matching notes there is no Apply or pretend fill. Editing, history, navigation, replacement, dismissal or cancellation invalidates the old action. Recheck, solved and stalled never select an answer digit.

Pause stops the clock and entry. Relaxed play has no mistake limit; challenge ends at three mistakes and may continue relaxed. New/import verify before replacing play; cancel or bounded failure retains the active board. If another tab changes saved progress, download either copy before explicitly replacing the exact reviewed baseline. Links share only the clean code, never progress, timer or answers.

Print the original clues

Use Print board beside play. Default output contains original diagonal clues and blocks only. Entries and notes are independent opt-ins; no answers, certificates or save envelope are printed. Preview captures an immutable board and snapshot. Opening, closing or canceling does not edit history, pause or rewind the ordinary timer.

Choose portrait A4 or US Letter at 100%, browser headers/footers off. Dark outlines, diagonal clues and hatched blocks work with printed backgrounds off. Bring the sheet to a friend and explain why an intersection works before filling a digit.

Daily and archive

Daily Kakuro and the published archive contain real immutable native publications. Missing dates stay unavailable; reading never generates or backfills. Only the persisted exact code/date association grants daily provenance. Optional local activity is off until enabled, and counts deliberate completion, never imports or history replay.